离散Sturm-Liouville单调型方程解的渐近性质

Q4 Mathematics

Tatra Mountains Mathematical Publications Pub Date : 2023-06-01 DOI:10.2478/tmmp-2023-0014

Janusz Migda, E. Schmeidel

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引用次数: 0

摘要

摘要我们研究了形式为Δ（rnΔxn）=anf（xσ（n））+bn的离散方程。\Delta\left（｛｛r_n｝\Delta｛x_n｝｝\right）={a_n}f\left（｛x_｛\sigma\left（n\right）｝｝\right）+｛b_n｝。利用Kaster-Tarski不动点定理，我们研究了具有规定渐近性质的解。我们的技术使我们能够控制近似程度。特别地，我们给出了关于解的调和近似和几何近似的结果。

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Asymptotic Properties of Solutions to Discrete Sturm-Liouville Monotone Type Equations

Abstract We investigate the discrete equations of the form Δ(rnΔxn)=anf(xσ(n))+bn. \Delta \left( {{r_n}\Delta {x_n}} \right) = {a_n}f\left( {{x_{\sigma \left( n \right)}}} \right) + {b_n}. Using the Knaster-Tarski fixed point theorem, we study solutions with prescribed asymptotic behaviour. Our technique allows us to control the degree of approximation. In particular, we present the results concerning harmonic and geometric approximations of solutions.

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来源期刊

Tatra Mountains Mathematical Publications Mathematics-Mathematics (all)

CiteScore

1.00

自引率

0.00%

发文量